TPMS fault... Probably needs new sensors (they have a finite life due to batteries), or maybe the last time tires were changed, sensors were not installed at all.
As for the check engine fault, impossible to diagnose unless you can provide the codes. Get a cheap OBD-2 reader, plug it in when the light comes on, and tell us the codes that come up. As for the 40MPH limit, usually the display will say "limp home" or something if it's reduced speed. Have you checked oil levels in the transmission? Low transmission oil will trigger limp home. However, could be anything really - need those OBD-2 codes!